I have successfully repaired speakers in that condition by replacing the rubber. They work fine after that. You just need to find rubber speaker surround rings the right size - generally from an electronics or specialist speaker repair joint - and the correct glue. If there's none in the set, rubber cement will do. I used Shoe Goo on mine.

Pick away as much of the rotted rubber as possible with a sharp craft knife, without damaging the cone - including where it sticks to the metal (or plastic) speaker driver body. The surround glues to the rear side of the paper cone - I got that wrong on my first one

Here's a set for reference.